(a) Find $k$ so that $f(x) = \begin{cases} \frac{x^2 - 2x - 3}{x + 1}, & x \neq -1 \\ k, & x = -1 \end{cases}$ is continuous at $x = -1$. OR (b) Check the differentiability of function $f(x) = x|x|$ at $x = 0$.